Prove that sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)
We know that 1. sin(a+b) = sin(a)cos(b)+sin(b)cos(a) and 2. sin(a-b) = sin(a)cos(b)-sin(b)cos(a) Add equations 1. and 2. sin(a+b)+sin(a-b) = 2sin(a)cos(b)+sin(b)cos(a)-sin(b)cos(a) = 2sin(a)cos(b) Let x=a+b and y=a-b, hence x+y=2a so a=(x+y)/2 and x-y=2b so b=(x-y)/2 Therefoe sin(x)+sin(y) = 2sin((x+y)/2)cos((x-y)/2)
AV
Related Maths A Level answers
All answers ▸Differentiate with respect to x: i) y=x^3ln(2x) ii) y=(x+sin(2x))^3
Find the gradient of the curve y=sin(x^2) + e^(x) at the point x= sqrt(pi)
Given that sin(x)^2 + cos(x)^2 = 1, show that sec(x)^2 - tan(x)^2 = 1 (2 marks). Hence solve for x: tan(x)^2 + cos(x) = 1, x ≠ (2n + 1)π and -2π < x =< 2π(3 marks)
Differentiate the following, y=(2x-4)^3